I ride down to -20F with Sigma BC 16.12 There may be some update by now of this computer. Battery operation has not been a problem in the cold. The screen has not been fading out at low temperatures, like for some other computers, and it has a backlight that does not cause a fade-out either.

Oops, I missed the wireless requirement. I presume there is a wireless version but I cannot attest its cold operation...